Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces

1. Front Matter

   Pages i-viii

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2. Introduction

   • Jürgen Berndt, Franco Tricerri, Lieven Vanhecke

   Pages 1-3

3. Symmetric-like riemannian manifolds

   • Jürgen Berndt, Franco Tricerri, Lieven Vanhecke

   Pages 4-20

4. Generalized Heisenberg groups

   • Jürgen Berndt, Franco Tricerri, Lieven Vanhecke

   Pages 21-77

5. Damek-Ricci spaces

   • Jürgen Berndt, Franco Tricerri, Lieven Vanhecke

   Pages 78-114

6. Back Matter

   Pages 115-127

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Generalized Heisenberg groups, or H-type groups, introduced by A. Kaplan, and Damek-Ricci harmonic spaces are particularly nice Lie groups with a vast spectrum of properties and applications. These harmonic spaces are homogeneous Hadamard manifolds containing the H-type groups as horospheres.
These notes contain a thorough study of their Riemannian geometry by means of a detailed treatment of their Jacobi vector fields and Jacobi operators. Some problems are included and will hopefully stimulate further research on these spaces. The book is written for students and researchers, assuming only basic knowledge of Riemannian geometry, and it contains a brief survey of the background material needed to follow the entire treatment.

• Generalized Heisenberg groups
• Riemannian geometry
• geodesic spheres
• geodesic symmetries
• harmonic spaces
• jacobic operators
• manifold

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